I don’t think it is a problem that Chabad is learning seforim of their Rebbe seriously. A response that sure many gedolim wrote something and this is light reading is strange. Obviously, leaders of our time address issues relevant to our time and it is worth studying in depth. Previous Torah is of course important and we can’t just red recent responsa without learning earlier material, but we are not resolving last centuries’ issues, but the current ones!
So, a possible problem arises when someone insists that everyone should learn their derech in a significant way, otherwise, why can’t they learn their own Rebbe and share that Torah with us?